Answer
both roots are imaginary.
Work Step by Step
For the equation $3x^2-2x+4=0$, we have $$a= 3, \quad b=-2, \quad c=4,$$ We check the value of the discriminant, as follows $$b^2 -4ac=4-4(3)(4)=4-48=-44$$ Since $-44$ is negative, then both roots are imaginary.
